Answered

Welcome to Second Life Answers, AMORPHES. As Luc has said, there is no way of appearing offline, not really. Not everyone uses Viewer 2, and some who do also own online trackers, so your true online status can always be seen. If you are wishing to have some peace and quiet when you log in, not having to answer to the IMs that inevitably come your way as soon as you log in, you can actually just ignore them. As said in another similar thread, true friends will understand your need for own space. If they don't, they are far too needy, and selfish, and you do not need to worry about hurting their feelings, as they are not showing you consideration by giving you some space.

Another of Luc's points is that for total peace and anonymity, where your main avatar WILL appear offline to friends, you can create an alternative avatar. Many people have them, just so they can explore or build, or shop in total peace.

Answered

Open your friends list, open a friends profile and choose permissions from the Actions menu.

But people who are in the same groups as you can still see you online, and people using some TPV's can still see whether you are online. There are also gadgets you can buy to see whether someone is online or not.

Best way to avoid being seen as online is to log in using an alt that your friends do not know about.

Answered

luc covered the most. i have just one thing to add - regardless of what viewer you or your friends use they can only send you a random im to "discover" you are online as they don't get the "user not online, message stored" message.